Approximation Theory

Engineering, finance, science, and many areas of mathematics itself
make use of quantities that are too complicated, too difficult, and
even too abstract to work with directly. A major goal of approximation
theory is to discover and analyze simple, easy to work with, concrete
quantities that can do a good, efficient job in their place - for
example, splines to fit messy curves, wavelets to analyze noisy
signals and to compress large images, and radial basis functions to fit
scattered data and serve as the ``approximation engine'' of neural
networks.

Graduate Program

The graduate program in approximation theory includes basic courses on
splines
MATH 657 and on foundations and methods of approximation theory
MATH 667, and advanced courses on applied harmonic analysis
MATH 658 and wavelets
MATH 668, as well as courses on a variety of
special topics.

Areas of faculty interest include radial and related basis functions,
scattered data surface fitting, rates of approximation, constrained
approximation, polynomial inequalities, wavelets, splines, and a
variety of other topics and fields. A list of involved faculty and
some areas each works in is included below, along with current PhD
graduate students.